fixed income 8: Yield and Yield Spread Measures for Floating-Rate Instruments

How are FRN coupons typically quoted?

MRR+Quoted Margin

e.g. MRR + 250 bps

What does “in arrears” mean for FRNs?

The reference rate is set at the beginning of the interest period, but payment occurs at the end.

What is the required margin?

The market-required spread over the reference rate needed for the FRN to trade at par on a reset date.

• aka discount margin

If quoted margin equals, is above, or belowrequired margin, what is the FRN price?

1. at par value on a reset date.

2. At a premium above par.

3. At a discount below par.

simplified FRN pricing model.

$$PV=\sum_{i}^{N}\frac{\frac{\left(MRR+QM\right)\cdot FV}{m}}{\left(1+\frac{MRR+DM}{m}\right)^{i}}$$

• PV = present value, or the price of the floating-rate note

• MRR = the market reference rate, stated as an annual percentage rate (it is sometimes known generically as Index)

• QM = the quoted margin, stated as an annual percentage rate

• FV = the future value paid at maturity, or the par value of the bond

• m = the periodicity of the floating-rate note, the number of payment periods per year

• DM = the discount margin = required margin stated as an annual percentage rate

• N = the number of evenly spaced periods to maturity

What defines a money market instrument?

A debt security with an original maturity of one year or less. Examples:

• Treasury bills

• Commercial paper

• Certificates of deposit

• Bankers’ acceptances

• Repos

How are money market yields different from bond yields?

• Money market: simple interest, annualized, not compounded

• Bonds: compounded, standard periodicity, time-value-of-money analysis

What are the two main quotation conventions for money market instruments?

1. Discount Rate (DR): interest included in face value, used for instruments like T-bills, commercial paper, bankers’ acceptances

2. Add-On Rate (AOR): interest added to principal, used for CDs, repos, floating-rate loans

pricing formula for money market instruments quoted on a discount rate basis.

$$PV=FV\cdot\left(1-\frac{Days}{Year}\cdot DR\right)$$

rearranged formula for discount rate

$$DR=\frac{Year}{Days}\cdot\frac{FV-PV}{FV}$$

pricing formula for money market instruments quoted on an add-on rate basis.

$$PV=\frac{FV}{1+\frac{Days}{Year}\cdot AOR}$$

Why does the discount rate understates the investor’s return?

Because the denominator in the DR formula is FV, not the investment amount (PV).

What is a bond equivalent yield (BEY) in the money market?

A converted rate that expresses a money market instrument yield on a 365-day add-on basis for comparison purposes.

How do you convert a discount rate to a bond equivalent yield?

1. Calculate PV from discount rate

2. Use PV in add-on formula to calculate AOR for a 365-day year

3. This AOR is the bond equivalent yield